(6x+1)(5x-3)=0

Solution for (6x+1)(5x-3)=0 equation:

(6x+1)(5x-3)=0

We multiply parentheses ..

(+30x^2-18x+5x-3)=0

We get rid of parentheses

30x^2-18x+5x-3=0

We add all the numbers together, and all the variables

30x^2-13x-3=0

a = 30; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·30·(-3)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*30}=\frac{-10}{60}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*30}=\frac{36}{60}
=3/5
$